Apparatus for resurfacing the cylindrical face of large drier drums

ABSTRACT

The present invention relates to an apparatus for refinishing the contoured surface of a substantially cylindrical Yankee drier drum without removing the drum from the paper machine. The invention is exemplified by an improved grinding apparatus consisting of a back stand grinder for forming the surface on the drum, a carriage upon which the grinder is movably mounted, a rigid cast iron bed with ways to guide the carriage parallel to the drier drum axis, means to traverse the carriage and a unique cam to control the movement of the grinder on the carriage in a manner which causes the grinder to generate the entire surface contour desired to be formed on the drum. The invention also includes the unique cam. The invention is further exemplified by a periphery on the grinder contact wheel contoured to adapt to the drum surface contour over the entire face of the drum.

United States Patent 1 91 1111 3,889,424

Buhayar et al. June 17, 1975 [54] APPARATUS FOR RESURFACING THE 3,546,817 l2/l970 Shaller 5l/49 CYLINDRICAL F 0 LARGE DRIER 3,6l6,578 ll/l97l Clark 5l/49 DRUMS Primary ExaminerAl Lawrence Smith [75] Inventors: Eric S. Buhayar, Swarthmore, Del.; Assistant Examine, Nicho|as Godici Gordon Gerstenknmi Springfield Attorney, Agent, or Firm-R. Duke Vickrey; William J. Foley [73] Assignee: Scott Paper Company, Philadelphia,

Pa. [57] ABSTRACT [22] Filed: May 20, 1974 The present invention relates to an apparatus for refinishing the contoured surface of a substantially cylin- PP 469,738 drical Yankee drier drum without removing the drum Related Appficafion Data from the paper machine. The invention is exemplified by an improved grinding apparatus consisting of a [63] Continuation of Ser. No. 179,69l, Sept. 13, I97], back stand grinder for forming the Surface on the abandoned.

drum, a carriage upon which the grinder 1s movably 52 us. c1 51/491- 51/101 R- 51/147- med, 3 bed with ways gfide 51116589 carriage parallel to the drier drum axis, means to tra' 51 1111. c1 B24b 5/16; B24b 51/00 the carriage and a unique cam [58] Field of Search 51/49 145 147 251 I65 89 movement of the grinder on the carriage in a manner SW16! 1 l which causes the grinder to generate the entire surface contour desired to be formed on the drum. The invention also includes the unique cam. The invention is [56] References Cited further exemplified by a periphery on the grmder UNITED STATES PATENTS contact wheel contoured to adapt to the drum surface contour over the entire fa e of the drum 2,466,123 4/1949 Osplack 5l/49 3,456,394 7/1969 Welsh 51 49 x 9 Claims, 6 Drawing Figures e 111001.15 REGION END 110 Hlk SHEU

PATENTEDJUN 17 1915 206mm 5S5 INVENTOR. Eric S. Buhoyor PATENTEDJUN 1 7 I975 SHEET 3 PRIOR ART INVENTOR.

Fig. 3A

PATENTEIJJUN 17 ms 3 8 89 L424 sxw 4 INVENTOR.

F'ig 4 Eric S. Buhoyor BY 0': v.

{r22 korn I I 2 ATTORNEY.

APPARATUS FOR RESURFACING THE CYLINDRICAL FACE OF LARGE DRIER DRUMS This is a continuation of application Ser. No. 179,691, filed Sept. 13, I97], now abandoned.

BACKGROUND OF THE INVENTION The invention relates to an apparatus and method for forming a complex-contoured surface on the cylindrical face of large drier drums, such as those referred to as Yankee driers and used in paper manufacturing. More specifically the invention relates to resurfacing in-place Yankee drier drums which have experienced wear from operating use. The invention enables sub stantially automatic refinishing of the entire surface of the drum with greater precision, speed and efficiency than with previously known systems.

The function of the Yankee drier in papermaking is to dry a moving web of paper during the brief period of time the web is in contact with the steam-heated Yankee drier. The wet web of paper, after removal from the forming wire of the paper machine, is pressed onto the surface of the rotating Yankee drier drum by a pressure roll. After rotating in close contact with the drier drum for a partial revolution, the dried paper is separated from the drier drum and creped by a doctor blade.

It is important that the pressure exerted on the paper web by the pressure roll be uniform across the full width of the paper web. Otherwise, a number of deleterious results can occur, such as variations in paper thickness, uneven drying, and uneven creping. If the pressure roll and the drier drum were both perfect cylinders under operating conditions, uniform pressure would easily be accomplished. However, this desired shape is not easily maintained under operating conditions because the drum and pressure roll are subjected to distortions from a number of mechanical and thermal operating forces. For example, the force of the pressure roll against the drier drum causes distortions in both their contacting surfaces, just as it would with another pressure roll cooperating in a calendering function. And it is well known in the art that two pressure rolls pressed against each other deflect each other. The same deflection is found in a simple beam held at both ends and subjected to a uniform pressure across its length. The center of the beam deflects more from the pressure than the ends because it is farther from the supports. The deflection configuration along the length of the beam is easily computed, as it also is with simple pressure rolls.

The operating distortions in a Yankee drier drum are more complex than in a simple pressure roll. ln addition to the external pressure from the pressure roll, the drier drum is acted upon by thermal and internal pressure forces from the steam injected into the drum to supply heat. Distortion caused by thermal expansion is further complicated by temperature gradients in the drum resulting from the cooling effect of the wet paper web. The web does not cover the full face of the drum, and the surface temperature of the uncovered portions of the drum is higher than the covered portions. The higher temperature also extends somewhat into the covered portions of the drum. The result is that the drum experiences more thermal expansion in the end portions than it does in the center.

Other factors which cause significantly more complex distortion in a Yankee drier drum than in a simple pressure roll are the large ratio of drum diameter to drum length and the relatively small drum wall thickness. These factors and slight flexibility of the large end caps holding the ends of the drum produce more complex distortions than those of smaller diameter pressure rolls which are held by their substantially inflexible end caps. Thus, the distortion configuration in the end regions of the drier drum is more complex than in a simple pressure roll to an even greater extent than the center region.

Makers of pressure rolls have found that a simple solution to their operating distortion problem is to compensate for the anticipated deflection by varying the radius of the roll to form a crown with a contour exactly the opposite of the anticipated deflection contour. Although the operating distortion problem in the Yankee drier drum is considerably more complex than that in a simple pressure roll, it is known by those skilled in the art that the solution is basically the same. That is, the drier drums are formed with a surface configuration which compensates for the expected operating distortions. Some of the expected distortions can be computed, but others are more easily determined empirically. It has been found that a combination of computations and empirical determination is the most expedient method of determining the overall drum surface distortion.

The production of a satisfactory compensating crown profile is further complicated by the desirability, while forming it, of partially simulating some of the conditions producing distortions under operating conditions. Thus, the net compensation required at the time of forming the surface of a Yankee drier drum represents the difference between the total compensation needed for operating condition distortion and that portion of this compensation which it has been possible to simulate at the time of forming. Thus, for example, a reasonable compromise is to duplicate operating thermal expansion, at least in the middle region of the drum. This can be done by heating the drier drum with steam at a lesser pressure than the usual operating pressure. The cooler steam is used to compensate for the absence of cooling from the wet paper web on the drum in operation. Of course, under these conditions, the drum distortion from internal pressure is not a duplicate of the operating distortion due to that cause, and the differences must be compensated for in forming the surface.

It is these compensations which cause the required surface contour to be formed on Yankee drier drums to have a unique complexity, especially in the end regions. And it is this unique complexity that prevents most existing resurfacing equipment from being entirely satisfactory for use in the resurfacing of inplace Yankee drier drums.

Most equipment used for grinding rolls and drums is unsuitable for resurfacing Yankee drier drums for several reasons. Yankee drier drums are quite large, up to 15 ft. in diameter, 17 ft. long, and weighing upwards of 100,000 pounds. Once installed in a papermaking machine, it is impracticable to remove them except under extreme circumstances. Therefore, satisfactory grinding equipment must be capable of resurfacing the Yankee drier drum while the drum is mounted in its operating position. It is also impracticable to leave the grinding equipment permanently mounted at the Yankee drier, not only because of interference with normal papermaking operations and potential damage to the precision grinding equipment by the enviroment of an operating paper machine, but also because of the high investment cost of providing each Yankee drier with its own grinder.

On the other hand, the use of a single grinding machine to resurface a number of Yankee drier drums presents the problem of adapting the machine to the various drum sizes and contours which each drum uniquely requires. This problem is further complicated by each resurfacing of the same drum requiring a slightly different contour than the previous resurfacing. This is due to the change in the operating distortion pattern of the drum caused by the decrease in drum wall thickness naturally accompanying each resurfacing operation. It is therefore apparent that a practicable and satisfactory grinding machine to resurface multiple Yankee drier drums must be readily movable from one drum to another and must be readily adaptable to form a different surface contour for each resurfacing job. It almost must be capable of forming the complex contours required in the end regions of the drum, a task most can only perform as a separate hand-controlled operation.

DESCRIPTION OF THE PRIOR ART One apparatus designed for in-place resurfacing of Yankee drier drums is disclosed in US. Pat. No. 2,579,39l and again referred to in US. Pat. No. 3,264,749. This apparatus consists basically of an endless abrasive belt revolving about a cylindrical form roll which guides the belt against the drum surface. The form roll has the reverse of the contour desired to be formed on the Yankee drier drum and the belt is moved along the form roll to generate the desired surface contour on the drum. A number of shortcomings in this apparatus are apparent. For example, the apparatus is not readily adaptable to form the different surface contour required for each job. The contour formed by this apparatus is dependent upon the contour of the cylindrical form roll, and the form roll probably represents a major portion of the cost of the apparatus, not only because of its size, having to be as long as the drier drum to be resurfaced, but also because of the close tolerances required in manufacturing it. it can be readily appreciated that the precision of the resurfaced contour on the drier drum can be no greater than the contour precision on the forming roll. Because each resurfacing job requires a different contour, it also requires a different forming roll. Although it is possible that a single form roll can be used for all resurfacing jobs on a single drier drum by making small contour changes to the forming roll for each job, a substantial cost is still involved in making the changes because of the high precision machining required on a large workpiece.

Another shortcoming apparent in this apparatus is the lack of precision caused by the same deflection in the middle region of the forming roll as that found in pressure rolls pushing against each other. As with pressure rolls, the forming roll can be designed to compensate for this deflection, but only at additional complication and expense.

Another apparatus designed for in-place resurfacing of Yankee drier drums is a portable grinder manufactured and sold to the industry by Farrel-Birmingham Co., lnc. This apparatus consists briefly of a back stand grinder, a carriage upon which the grinder is mounted and a massive cast iron with ways to guide the carriage parallel to the drier drum axis. The whole apparatus is portable and requires the bed to be mounted adjacent the drier drum for each resurfacing job, taking care to precisely align the ways on the bed with the drum axis. The carriage is automatically traversed along the ways by a motor driven pinion and rack. The back stand grinder, consisting of an abrasive belt which wraps a motor driven contact wheel having a slightly resilient surface and a back stand wheel, is pivotally mounted on the carriage so that angular movement of the grinder about the pivot moves the grinder contact wheel toward or away from the drier drum axis. The movements of the contact wheel toward and away from the drum axis as the grinder carriage traverses the length of the Yankee drier drum control the drum surface contour. This motion of the grinder cound be completely hand controlled by a screw crank. However, it is far more satisfactory to control the motion by means of a cam and cam follower mounted to the back stand grinder. The cam is designed to cause the desired component of motion radial to the drier drum axis even though the pivoting motion of the grinder is not necessarily in the same direction. A rack and pinion controls the rotation of the cam through a gear reducer in a predetermined relationship to the movement of the carriage along the bed. An eccentric circle cam of adjustable eccentricity has been found satisfactory for forming the typically desired contours on Yankee drier drums over about the middle of their face lengths.

The Farrel-Birmingham grinder satisfies two of the beforementioned requirements for a practicable and satisfactory inplace resurfacer of Yankee drums. It is readily movable from one drum to another, and it is readily adaptable to form a different surface contour for each resurfacing job by merely changing the eccentricity of the circular cam. However, in the past, the grinder has not been capable of forming the complex controus required in the end regions of the drum except by manually controlling the radial movement of the grinder. It had been considered far too complex and time consuming to design cams which could control the complex surface forming in the end regions of the drum. This was especially true when considering that such cams would be usable for only one resurfacing job. Therefore, the past approach has been to use an eccentric circle cam to control forming of the middle portion of the drum and hand control for forming the end regions. This approach was not entirely satisfactory, because of the complication of switching from hand control to cam control or vice versa as well as the unpredictable accuracy inherent in trial-and-error operations.

Past practice has been to first grind down the middle 80% of the drum using the eccentric cam control to form the desired contour and then to form the end regions by hand control. The middle portion is ground in passes following the desired contour until all worn surface is removed over that entire portion. Then the end regions are ground down to a matching extent. lf excessive surface deterioration still prevails at the end regions and grinding to a greater surface depth is required, then the middle region must be reground to bring its contour into conformity with the end regions. Regrinding the middle region drastically increases total grinding time, resulting in increased down time for the papermaking machine at a loss of some hundreds of dollars per hour in lost production. There is considerable pressure on the grinderman to finish his job as soon as possible, and therefore, it is only natural that he tends to grind more than is necessary in the middle region of the drum to avoid possible regrinding later. The unfortunate result of grinding more than necessary is a shorter life for the drier drum. Eventually the drum thickness is reduced to a point where the drum has to be replaced, at a cost of several hundred thousand dollars. Typically, seven or eight resurfacing jobs are all that are usually realized.

it takes little imagination to realize the advantage of extending the life of a drier drum even by one grind. Additional life can be gained by grinding only the minimum necessary depth on each resurfacing job, but this can be done only if the end regions are ground concurrently with the middle region. That is, each grind pass is from end to end of the drum. To attempt this with hand control in the end regions and cam control in the middle region has not been found practical.

Yet a further problem is presented in grinding the end regions concurrently with the middle region. The contact wheel axis is maintained parallel to the axis of the drier drum throughout the entire traverse pass across the drum face, but the desired surface contour of the drier drum is not parallel to its axis at all locations. The deviation is especially severe toward the ends of the drum. Therefore, if a contact wheel having a right cylindrical periphery is used to press the abrasive belt against the drum surface, only one corner of the grinding surface is pressed against the drum surface when grinding each end region despite the slight resiliency built into the contact wheel surface. In the past, this problem has been solved by beveling the contact wheel periphery to approximately match the contour of one end region of the drum when grinding that end, and beveling the contact wheel in the opposite direction when grinding the other end of the drum. Of course, the contact wheel periphery was unbeveled for grinding the middle portion of the drum. More precise grinding could be accomplished by dividing the drum into five zones rather than three and using a different bevel angle on the contact wheel for each zone.

Changing the bevel on the contact wheel meant either changing the contact wheel or machining a new bevel on the same contact wheel for each zone. Either way the drum grinding process was interrupted and a continuous grind pass could not be made from end to end of the drum. The tendency was to completely grind each zone before going to the next zone, which frequently resulted in overgrinding and the resulting waste of drum life.

It can be seen from the foregoing discussion that prior art techniques for resurfacing Yankee drier drums in-place have all suffered from one or more shortcomings, such as inability to make continuous grind passes from end to end of the drum, inability to automatically form the contours in the end regions of the drum, lack of precision, excessive time consumption, and lack of practicable adaptability to forming the different surface contour required for each job. The advantages of overcoming these shortcomings are substantial, resulting in shorter down time of paper machines for resurfacing jobs, less material removal on drum walls during each resurfacing and thus longer drum life, and more precise surface contours which enable production of higher quality paper. It should also be noted that quicker resurfacing jobs with less surface removal would encourage more frequent refinishing. Because pitting and other deterioration of the drum surface proceeds into the drum wall at an exponential rate, it is possible that reducing the time between refinishing jobs to say one-half of the usual period, for example, could reduce the amount of surface material to be removed to much less than one-half of the usual amount. Thus, the resulting life of the drum could be further increased and the average quality of paper produced improved.

Having in mind the shortcomings of the prior art techniques for resurfacing Yankee drier drums and the advantages of overcoming these shortcomings, it is an object of the invention to provide an apparatus for forming the surface of a Yankee drier drum in-place by making continuous, uninterrupted grind passes from end to end of the drum. A further object of the invention is to provide an apparatus in which the contour forming of the entire face of the drum including the end regions is substantially automatically controlled with greater precision than with prior apparatus. Another object of this invention is to provide an apparatus which is capable of practicable use with divers Yankee drier drums and inexpensively adaptable to forming the different surface contour required for each resurfacing job.

SUMMARY OF THE INVENTION According to the present invention the portable grinder of the type available from Farrel-Birmingham (30., Inc. and discussed in the preceding background of the invention is improved to overcome the above-mentioned shortcomings of the prior art. The improvements feature two major changes, a new, unique cam capable of controlling surface formation on the Yankee drier drum in the end regions as well as the middle region and a contoured contact wheel. The new cam is designed by a computer from tabular information about the desired contour to be formed on the entire surface of the Yankee drier drum to be resurfaced, along with certain critical dimensions of the grinder apparatus to be used and its placement with respect to the Yankee drier. The computer converts this infonnation into a punched tape to be used in a Numerical Control milling machine which cuts the desired cam. For each resurfacing job, the required data is inserted into the computer program, a punched tape is produced, and the desired cam is quickly manufactured with great precision and little cost. This method avoids the complex and time consuming and calculating steps of computing a cam design for the ends of the drum and the great expense and delay of producing a master cam according to that design with standard tool room techniques, along with the probable inaccuracies inherent in such procedures, if it were even possible within practical limitations to produce the cam in this manner.

Even the new unique cam does not alone overcome all of the shortcomings of the prior art. The full advantage of continuous grind passes from end to end of the drum cannot be satisfactorily realized with the old style, right-cylindrical-periphery contact wheel. Therefore, especially satifactory results can be obtained by use of a contact wheel with a contoured periphery that allows portions of the contact wheel inwards from its edges to match the surface contour of the drier drum at all positions from end to end of the drum. The periphery contour is in the form of a circular arc. The slight resiliency of the contact wheel surface then tends effectively to expand the theoretical point contact in all directions into an area contact achieving high metal removal rates by the abrasive belt.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a front elevation view of the grinding apparatus of the invention in position to resurface a Yankee drier drum shown with a greatly exaggerated surface crown profile for illustrative purposes.

FIG. 2 is a side elevation view of the illustration of FIG. 1 as viewed in the plane of the lines 2-2 and in the direction of the arrows.

FIG. 3 is a plan view of the contoured contact wheel of this invention shown contacting the surface of a Yankee drier drum in several positions, the drum surface crown profile being shown greatly exaggerated for illustrative purposes.

FIG. 3A is a plan view of the prior art contact wheels shown contacting the surface of a Yankee drier drum shown with a greatly exaggerated surface crown profile for illustrative purposes.

FIG. 4 is a diagrammatic view of the illustration of FIG. 2, showing the dimensions used to compute the cam design.

FIG. 5 is a diagrammatic view of the cam of this invention with the cam cutter and cam follower shown to illustrate considerations in programming the path of the cam cutter.

DESCRIPTION OF THE PREFERRED EMBODIMENT The grinder apparatus which exemplifies the invention is illustrated by FIGS. 1 and 2 where two views of the apparatus in position to resurface a Yankee drier drum are shown. The grinder apparatus has three major parts, the backstand grinder 7, the carriage 8, and the bed 9. The backstand grinder 7 consists of the grinder base 11, the grinder 12, hand adjustment means 14 to position the grinder frame 12 on the grinder base 11 along grinder head in-feed ways 10, a contact wheel 15 and backstand wheel 16 both mounted on the grinder frame 12, an abrasive belt 17 mounted about the contact wheel 15 and backstand wheel 16, and means for driving the abrasive belt 17, illustrated here by motor 18 driving the contact wheel 15. The grinder base 11 is attached to the carriage 8 at the pivot mounting 19 and rotatable about that mounting. The carriage 8 rides against flat way 21 and vee way 22 on the cast iron bed 9. The ways are aligned parallel to the axis 32 of the drier drum 24. The drier drum 24 is mounted upon a shaft on axis 32 and which is in turn rotatably held by bearings 6. The carriage 8 is traversed along the ways 21 and 22 by drive means illustrated here as rack 26, pinion 24, and reduction gear motor 25 attached to the carriage 8. The traverse speed of the carriage 8 is controlled by the speed of motor 25.

Mounted on the carriage 8 is a cam 27 which is rotated in relationship to the traversing movement of the carriage 8. In FIG. 2, part of the carriage has been removed to expose the cam rotational means. The cam rotational means is exemplified here by rack 26 and pinion and worm assembly 28 driving the cam 27 through the worm and worm wheel mounted on the shaft 29. The gear ratios in the cam rotational means are such that the cam 27 makes somewhat less than a full revolution when the carriage 8 traverses the full width of the Yankee drier drum 24.

On the end of the grinder base 11 opposite the pivot mounting 19 is rotatably mounted a cam follower 31. The cam follower 31 rests upon the cam 27 and is moved up or down in relationship to the cam contour as the cam rotates. The cam follower movement swings the grinder base 11 in an angular movement about the pivot mounting 19 which causes the contact wheel 15 to move closer or farther from the axis of the drier drum 24. Therefore, by use of a properly designed cam, the path of the contact wheel as the carriage is moved across the face of the drier drum will form the desired surface contour of the drier drum.

A typical resurfacing operation is carried out in the following manner. First, the cast iron bed 9 is mounted to the floor beside the drier drum 24. Next, the carriage 8 with the attached grinder 7 is placed in the ways 21 and 22. It is essential that the bed ways 21 and 22 be both straight and aligned with the axis 32 of the drum 24 because any error will be passed on the drum surface contour as it is formed. The carriage 8 is then traversed along the ways until the contact wheel 15 is opposite the center 33 of the drum 24. This is the point where the radius of the drum 24 is to be the largest. The cam 27 is then oriented so that the center point on the cam is in contact with the cam follower 31 and is then locked to its rotational drive. The grinder frame 12, holding the contact wheel 15, backstand wheel 16, and abrasive belt 17, is slid up along the grinder head infeed ways 10 on the grinder base 11 by the hand adjustment means 14 until the abrasive belt 17 contacts the drum surface 24. The rotation of the abrasive belt 17 is then started. Any of the operating conditions which are to be simulated during the grind have meanwhile been put into effect, and the apparatus begins its first grind pass. The slowly rotating drier drum 24 exposes its entire surface to the grinder. When the carriage 8 reaches the end of the drum 24, its direction is reversed either by reversing the motor direction or by other means well known in the art.

During the grinding process it will be necessary to periodically move the grinder frame 12 closer to the drier drum 24 as the grinder pressure on the drum drops off due to metal removal from the drum and breakdown of the abrasive belt. These adjustments are performed by those skilled in the art upon observing changes in the power consumed by the abrasive belt drive motor 18 and can be made while traversing the carriage 8, so there is no need to stop the grinding operation. It will be necessary, however, to periodically change the abrasive belt 17 as it wears. The grinding operation is stopped when all defects in the drier drum surface have been removed. Final passes can be made with abrasive belts having finer grit so as to produce a smooth polish on the Yankee surface.

The surface of the contact wheel 15 is composed of a slightly resilient material, such as hard rubber, and therefore, can be compressed slightly when pushing the abrasive belt 17 against the drum surface. Compressing the resilient contact wheel 15 against the drum surface accomplishes various beneficial results because the contact wheel can expand slightly if necessary and still maintain pressure between the abrasive belt 17 and the drum surface. One such result is the larger area of contact caused by the contact wheel 15 compressing against the drier drum 24. And another result is the higher contact pressure between the abrasive belt 17 and areas of the drum surface which require more material removal. This increases the metal removal rate to bring such areas into conformity with the desired contour being generated elsewhere. The converse is also true with areas of the drum surface which require less metal removal. Furthermore, in actual practice the grit on the abrasive belt 17 is continuously breaking down and the contact wheel must be advanced manually to compensate for this loss of belt thickness as well as for the metal thickness removed from the Yankee drier. The expansion of the compressed contact wheel enables the grinding operator to perform this manual advancing operation periodically rather than constantly.

Referring now to FIG. 3, the contoured contact wheel of the invention is illustrated pressing the abrasive belt 17 against the surface of the drier drum 24 in two positions (only part of the contact wheel is shown). Only part of the drier drum surface is shown because the crown contour is symmetrical about the center line 33 of the drum and the side of the drum not shown is a mirror image of the side shown. Contact wheel 150, having the contoured periphery of the invention, is shown at the center 33 of the drum 24 where the theoretical contact point 34 between drum and abrasive belt is at the center of the contact wheel. Contact wheel b, also having the contoured periphery, is shown in the end region of the drum 24 where the theoretical contact point 35 between drum and abrasive belt is off center of the contact wheel.

FIG. 3A illustrates two contact wheels of the prior art against the surface of the drier drum 24. As in FIG. 3, only parts of the contact wheel and the drier drums are shown in FIG. 3A. Contact wheel 15c, with abrasive belt 17, illustrates the adverse corner contact which would occur in the end regions of the drum were a right cylindrical periphery contact wheel to be used. Contact wheel 15d, also with abrasive belt 17, illustrates the beveled-edge contact wheel of the prior art. It can be readily seen that neither the square-edged nor the beveled-edge contact wheel is suitable for use over the entire drum surface. It should be noted that this circular contoured periphery indicated as having a radius D( 13) and illustrated on contact wheels 15a and 15b is the most desired contour, not because of the compressibility of the contact wheel, the contour can be approximated with good results by an appropriate series of straight lines.

It can be seen from FIG. 3 with the contact wheel in positions such as is contact wheel 15b where the contact point 35 is offset from the center of the contact wheel, an allowance must be made when designing the cam to account for the distance 36 by which the center point of the contact wheels periphery is to be held away from the desired Yankee surface so that contact point 35 generates the surface correctly as it sweeps by.

Thus a finite width contact wheel must be advanced a somewhat lesser distance towards the Yankee surface than consideration of its center line radius alone would dictate. This correction is essential to obtaining a precise surface contour on the drum.

Referring again to FIG. 3, the size of the radius of curvature of the contact wheel 15 periphery, indicated as D( 13), has been found to be very important to optimum use of the invention. Its size is dependent upon the mixture crown slope of the Yankee drier drum 24, which will be located at the extreme drum positions.

For example, the maximum desired crown slope on one particular Yankee drier drum, having a l2 ft. diameter and a 15 ft. 8 in. length, was determined to be 0.00628 inches per inch. And for resurfacing that particular drum, a contact wheel 15 having a wheel width of 4 inches works well with a periphery contour radius D( 13) of 240 inches. This radius D( 13) design is based upon two objectives. First, the periphery must have an area with a slope equal to or greater than the maximum crown slope on the drier drum 24; this objective alone can, of course, be easiest accomplished with the smallest possible radius D( 13). And second, the radius should be as large as possible to allow the greatest possible contact area between the wheel 15 and abrasive belt 17 and the drum 24.

The theoretical contact point of the crowned contact wheel with the drier moves away from the center of the wheels face as the drier profile slope increases. At the maximum drier profile slope it is highly desirable that this theoretical contact point has not yet reached the edge of the contact wheel so that the point may expand in all directions into an area contact. Thus, with a 4 inch face wheel it might be deemed appropriate to match the maximum drier profile slope 1% inches out from the center of the wheels face for a contact wheel of typical resilience. The crown radius D( 13) required to achieve this can be estimated from the following formula:

D(l3) =1 l l H8 =t/S (Because S is very small compared to l) where D(l3) crown radius (inches) t= distance out from center of wheels face (inches) S maximum drier profile slope to be matched (inches/inch) The advantages of the invention depend heavily upon the proper design of the cam 27. In the past, it has been found feasible to cam control drum contour forming only in the middle or so of the drum, noted in FIG. 1. The contour in the end regions, also noted in FIG. 1, was formed by manually operating the hand adjustment means 14. Now, through use of a unique computer program it is easy to compute a large number of X/Y coordinates for successive positions of a milling cutter which will generate the desired cam on a Numerical Control milling machine. Transforming these coordinates into punched tape instructions for such a numerical control milling machine can be effected in various ways, well known to those skilled in the art, each way being particularly adapted to the particular numerical control milling machine being used. In the preferred form of this invention, a Compudyne milling ma chine is used and results in an inexpensive and speedily manufactured precision cam. The cam is designed to move the grinding surface to generate the contour desired for the entire drier drum. The contour, determined for each resurfacing job by a combination of computations and empirically derived adjustments, is expressed as a crown table of radial dimensions for every inch say of linear distance from the center line of the drum to one end. The contour for the other half of the drum is symmetrical and need not be included in the table. The determination of the crown contour is not part of the invention, but is determined by methods well known in the art.

In designing the cam, the computer performs several tasks which convert the desired crown table to a cam design. In doing so, certain dimensions of the grinder apparatus and its positioning must be considered. These dimensions are illustrated by FIG. 4 which diagrammatically shows the drier drum 24, the contact wheel 15, pivotal mounting l9, flat way 21, vee way 22, earn 27 and cam follower 31. The dimensions shown are as follows.

D(l) is the radius of the drier drum 24 on center line 33 of the drum. (inches) D(2) is the vertical distance of surface of flat way 21 of grinder bed below axis 32 of the drier drum 24. (inches) D(S) is the horizontal distance between the center line of vee way 22 of the grinder bed and the axis 32 of the drier drum 24. (inches) D(4) is the diameter of the contact wheel on its center line and including the abrasive belt 17 thickness. (inches) D(S) is the radius of cam 27 surface at setting for center line 33 of drier drum 24. (inches) D(6) is the maximum diameter of curved-face cam follower 31. (inches) D(7) is the angle to horizontal of grinder-head infeed-ways 10 with the cam at D(S) setting. (degree) D(8) is the horizontal distance between center line of vee way 22 of grinder bed 9 and vertical line through center of grinder carriage pivot 19. (inches) D(9) is the horizontal distance between center line of vee way 22 of grinder bed 9 and vertical line through contact point of cam follower 31 with cam 27. (inches) D( 10) is the vertical distance of the surface of the flat way 21 of grinder bed 9 below horizontal through center of grinder carriage pivot 19. (inches) D(ll) is the distance perpendicular to grinder-head infeedways 10 between center of grinder carriage pivot 19 and path of contact wheel center as it is moved along the infeed ways 10. (inches) D( 12) is the grinder carriage 8 travel along ways 21 and 22 per revolution of cam shaft 29. (inches) D( 13) is the nominal radius of grinder wheel crown.

(inches) (note: D(l2) and D(13) are not shown on FIG. 4.

OUTLINE OF THE DESIGN TASKS PERFORMED BY THE PROGRAM Once the crown table and dimensional data have been acquired the cam advantage is calculated for the cam in the center-line-oi drum position. This is the cam rise required to produce a unity motion component of the contact wheel radially towards the drum and depends on parameters D(l) through D(4) and D(7) through D( l l This advantage ratio is used throughout even though the angle, which is D(7) at the center of the face of the drum, varies slightly as the crown is generated. The effect of the angle change is not considered significant in its effect on the motion of the contact wheel. The crown table is then modified to allow for the cam advantage. Next the crown table is modified to compensate for the difference 36 between the center point of the contact wheel's periphery and the effective point of metal removing action necessitated by crowning the contact wheel to a radius of D( 13) to allow it to match the flanks of the drum crown. Then the table is transformed into one of radial distance to the center of the cam follower.

Thereafter the table's treatment resembles that discussed in ASME Publication 66-MECH-2 which is of a manuscript entitled Computerized Cam Design and Plate Cam Manufacture by E. S. Buhayar and contributed by the Machine Design Division for presentation at the Mechanisms Conference, Lafayette, Indiana, Oct 10-12, I966, of The American Society of Mechanical Engineers. Briefly, the computer converts the radial distances to the center of the cam follower into the path required by the cam cutter to form the desired cam. The follower and cutter may have different diameters. The cam cutter path is then expressed in an X/Y grid coordinate system as indicated in FIG. 5. Referring to FIGS. 5, cam 27 is shown against the X/Y coordinate grid with respect to which the path 48 of the cam cutter 40 about the cam blank 41 is described. The contoured surface to be generated on the cam blank 41 is indicated by numeral 42. In the preferred form of the invention, the grid system is divided into a series of imaginary lines 46 parallel to the X axis and a series of imaginary lines 47 parallel to the Y axis.

The milling machine used in the preferred form of this invention is limited to successive movements of the cutter to a minimum of 0.001 inch in either the X or Y direction. This precision has been found satisfactory for making the cam, especially in view of the typical cam advantages of approximately 3 to l, which reduces any error in drum surface contour of one-third of the error in cam contour. If the cam cutter 40 is not the same size as the cam follower 31, the cam cutter path 48 must be adjusted to account for the fact that the point of contact 44 between the cam follower 31 and cam 27 is not on the line 45 passing through the center of the cam follower 31 and cam 27 in all cam positions.

The following discussion will be helpful in further understanding the computer program which determines the cam cutter path. The table of radial distances R to the center of the cam follower, converted from the crown table, is provided with cam rotational position values T generated from the factor D( 12) and the position of the grinder from the center line of the drier drum. Offsetting through each R point on the path of the center line of the cam follower normalto-the-chord is performed to get back variously to the X/Y coordinates of the cam surface and the center of the milling cutter. To do this adjacent points either side are used. The table is extrapolated at its terminal velocity until the sideways shifted cam-surface contact-point with the large diameter cam follower reaches the outside surface of the cam blank 50. If this occurs earlier than 6 inches beyond the edge of the Yankee as determined by the last value of the original crown table, the job is terminated with an appropriate message suggesting that D(S), the cam surface radius on the paper machine center line, be decreased.

If this test is passed, further constant velocity extrapolation occurs until the cam cutter center reaches the predetermined circular approach path 49. At this position the cam blank 41 is not being touched by the cam cutter 40. This allows high feed-rates to save manufacturing time. The job will be terminated if this radius is not reached. The message suggests increasing D(S). It is to be noted that the tape used to cut the cam contains complete instructions to move the cutter all the way around the cam blank and back to the starting point to afford an easy check on the correct functioning of the open-loop servocontrol of the Numerical Control milling machine used.

The results of the above extrapolation search provide the data required for synthesis of a six section cam comprising a dwell, a constant velocity and a table-ofvalues section which are mirror imaged around the other half of the cam.

The program generates this synthesis without user intervention. It then computes the outputs an X/Y coordinate deck in the appropriate format to be converted in the preferred form of the invention into a punched tape for instructing a Compudyne Numerical Control T IS P OGEA OUTLXNE W ANTS! X3|9 ND X301? TO AKE AJD LSO DATA (Al ROG A OUTLINE USES REQUIQEG SUCH AS Tt-AT was av FARREL-BlR-:

GRINDEQ'S POSITIONING QELATIVE TO milling machine. The punched tape issues signals to the milling machine to move the cutter by a long tain of appropriately directioned 0.001 inch stepping signals. The stepping signals can be one of eight different signals corresponding to the eight possible step directions to an adjacent grid intersection.

The punched tape is used in conjunction with a standard drawing which gives the cam blank dimensions and the set up instructions as well as the starting position/ending position (numeral 43, FIG. 5) and the size of the cutter to be used.

Having described the operations of the computer program used to design the unique cam of the invention, an outline of the program itself follows:

STA DARD FORTRAN NOTATION AS OEFI\ED P ESEYT T iE ALGORIT S AND SEQUENCES CALCULATIONS.

ROG A AKES DIAERSXO'QAL DATA RELATING TO A YANKEE DRIER INC A YANKEE BRIT- DRU W ICH IS TO BE GROUND TO A DESIRED PROFILE.

1T LSO TAKES A CROWN TABLE WHICH LISTS T? DESIRED VALUES OF THE QADIAL CQ'JWN AT SPECIFIED L lNE OUT TO ONE EDGE OF THE DRIER:

EQUAL INTERVALS FRO THE CENTER- HE DESIRED CMONNE OUT THE OTHER WAY IS ASSU ED TO BE SY -"ETQICAL- T E ROGRA 'S OUTPUT CONSISTS OF A TABLE OF SUCCESSIVE X/Y SORXINATES WHICH THE CUTTER OF A !U E QICAL CONTROL "'lLL ING AC INE SHOULD ASSU'WE TO CUT A CA FROM A CIRCULAR BLANK OU TED AT T E (ICOROINATE ORIGIN.

TFIS CA I5 FD? USE MAKES A SERIES OF FDGE TO EDGE If: CONTQOLLING THE GQliDE? '5 ACTION AS IT PASSES GENERATING THE DESIRED 'iOFILF ON A YANKEE DRIEQ DRU COiTROL SO E A'tTlCUL-A? NU-"E'=!ICAL CCNT'Q'JL ILLINQ:

DEFIR THEN PROCESS THE ABOVE ENTXOJED ADA TEC TO "'AC UE AS IT CLOSED PAT-i WHICH RETURNS TO ITS STLUTINL, pnzwr 53 A5 o WAKE THE ACTION OF OPEv-LOOP-SERVO EU E XCAL CC 'T -OL ILLING ACT-I'vES SELF CHECKING. TO S L-ED TH:

3 A ION THE CTRCULAQ A I RCACT A'\'D OEPA -ETUQE SECTIONS ARE DESIGNED vs-I TP TP'E CU ER OUT OF CC TACT WITH THE CA. BL NK- u OS -A STAQTS RY SETTIT, p 5) GLE-DI E SIGNAL A RAY SIZED AS CLLfL-JS u F WP) X MP1 I wHEQE TYDICALLY v.2 Zi-w] IS DE I IED n I a 0 NEXT TFE PQOG A ACOUIQES T E DATA ERTINEAT TO THE DARTICULAR J09 IIIOIIIOUI GEO4ETRY DATA- u a a D I 1 'DIUS O YANKEE Oi CENTERLINF CF PAPER ACHINE I INCHES) 0T2) VERTIC L DISTANCE OF SURFACE OF FLAT WAY OF GRINDER BED BELOW HORIZONTAL THROUGI" CENTER SF YANKEL I INCHES) D I 3) HORIZONTAL DISTANCE BETWEEN CENTERLI'WE OF GQIWDEQ BED VEE WAY AND VERTICAL TFROUGH CENTER OF YAN EE I INCHES I DH) DIA ETER OF GRINDER WHEEL CX ITS CENTERLINE AND IICLUI ING ABRASIVE BELT THICKJESSES I INCHES) 0(5) A'JIL-S OF CA" SURFACE AT SETTING FOQ CENTERLINE OF PAPER MACHIAE I I|\CHES) AXI L). DIAMETEP 0 CURVED FACE CAM FOLLOWER I INCHES) D I 7) ANGLE TO HORIZONTAL OF GRINDER-HEAD INFEED'WAYS WITH CA AT D( 5 l SETTING (DEGREES) D I 8) I HORIZONTAL DISTANCE BETWEEN CENTEQLINE OF GRINDER BED VEE WAY AND VERTICAL THROUGH CENTER OF GRINDER CARRIAGE IVGT l INCHES) (3(9) ORIZO'VTAL DISTAJCE P-ETLviE", CENTEQLI" E OF GEI JE BED VEE WAY AND VERTICAL T QOUGH CONTACT OINT CF CL'QVED- FACE C IILLOA'F' WITH CAM I I C EST F- 10 I TQTICAL DIST-1C5 C SUQFACE 3F FL WAY OF (BINDER BE;

EELJW ORIZCNTAL T 'QC'JGQ CE'\TE' SF (RINDEF; CA'QRI AGE IX O INCP-EST D I l l I OISTA CE PER E DICULA'? TO GFIxDE'Q-HEAO INFEEO-WAYS BE wFE' CENTEP OF GQI DER CARRIAGE IVOT AYD ATH OF G I JDER W EEL CENTE. AS IT IS DVED U I S INFEEC SLIDE I INC ES) .3 T 1? I GQINCF CA -I'QIAGE T'QAVEL ALONG ITS WAYS i? QEVCLUTIOR O T- 'E CA" SHAFT I IKCVES) l l 3 I O I AL "4A9 IUS OF T E G IWDE? WHEEL CRLM-H. IJCHL'S) C T/f A=LE DA A.- a 0 \v L H.1""BE C VALJLS SPECIFIED I T-E CRGA'N TABLE.

C EC'L 'ivE Ltwlm A "AY- 31 :MTIWF I 1 T AOIAI. C OWN A T E CE"-.TEF?LI 3E OF THE YA-Kfii T'? T A1 IAL. C'QOWN 9 11) T'E CENTERLI \E (F THE YANKEE (3 3 OIAL C OW 2*" F 7) T E CE' TE!?LI'E OF HE YANKEE (h l -TIIAL C 'OW\ 3*9 W HE CE 'E LIAE OF THE YANKEE ETC.

- (H/AL) QADIAL CROWN INVAL-1 'P FROM THE CENTERLINE OF YANKEE KOTE. on TPE CONVENTION IS TH T R I 1) 0O AND SUCCESSIVE VALUES ARE TO BE IT.- INCHES AND TO I'YCREASE POSITIVELY EVEN THOUGH THIS INDICATES METAL TO PE QE OVED RO THE YANKEE.

STAQT OF CALCULATIONS a n o u a 0 n CALCULATION OF RATIO. 0. 0o

QATIO TPE CAM ADVANTAGE WHICH IS THE CAN RISE REQUIQED TO PRODUCE A UNITY COMPONENT OF MOTION OF THE GQINDER WHEEL RADIALLY TOWARDS THE AXIS OF T E YANKEE.

X1 I DT'fH-PI I180.

X? I H) l 3 I-DI HSI \(Xl /COS4X1 I X3 I D lll I'SORTI (DIET-D18) I**24-X2*X2)/ (D I 3 )-DI? 1 T X0 l DUN- N 1O I-XZ-XB X7 SINHeHXA/H ATV? If) I F 1 +13 9) l /XIC TRA'KSFQRMATICN OF T-E C"W\ ASLF- 1 T E Q VALUES OF Th: ABLE ARE T iANSFOQMECJ INTO RAD! I TC THE CEH' F 3F TI E CA'-' FETLLOWER, ALL-NI\G EC PO T E CD- ADVAN AGE MD PC T -E CORECTICT= NECESSAR .ECAJSE OF COVACT ONT OFFSET DL'E T? T E G 'I DEQ WHEEL. CHOW? ADIUS- I E l .J-l I 11 a ll :12

l2 TAQD RAC'IFH? I JI-RP I l CO I SQRT TAND*TAND+@AD*?ADI-HAU 13 D95? RLJ) I J) QIJ I-COR IJI DIS' QATIO UJI l") CCNTINUE EXTENSION OF THE CAM SURFACE- a a o Tug \fFXT PAQT OF THE PQOGPAP IS CCNCERNED WITH CONTINUING THE CA SURFACE BEYCND WHEQE IT IS NEEDED TO GRIND THE YANKEE.

THIS EXT NSION IS ADE AT THE SAME RATE OF RISE A5 AT THE EDGE- F F-YANKEF TJSITION- THE NLJMRF? OF S EPS IS CALCULATED TO FIRST LOSS OF CUTTER CONTACT WITH THE CA FLA GK AND -1E\ TO CONTINUE ON OUT TO REACH TEE NON-MFTAL-CUTTI NG CIRCULAR APPROACH PATH OF T E CUTTER CEN ER.

TO DO THIS IT IS NECESSA Y TO QFFSET THE CENTER OF THE CAM DLLOWF? ER ENDICULAR TO ITS PATH BY THE CAM EOLLOWER RADIUS =0 T- E FIQS ART OF THE ASK AND BY THE DIFFEREICE BETWEEN THE CA FOLLCWEQ ANT CUTTER QADII FOP THE SECOI\D ART- IT IS TH E OTED THAT THE SI ILAR TR IANGLE B SED COORDINATE SEOAETRY USED EFE'KS TO A X/Y COORDINATE SYSTE. UNIQLE TO T -El5E TASKS AND \OT TO BE CCIFUSED v-I TH THAT USED TO EXPRESS TH? CA P OFILEu 29 CCWTINUE CALCULATING R VALUES FOR EXTENSION. a u 0 0 DO 30 J=l IRCUT \VAL'MJ Q T "4) Q T VAL 1 *J'WST 30 CONTINUE NOTE- ONE EXTRA PLACE OF T E R ARRAY HAS BEEN FILLED FOR USF IN UPCO ING OFFSETTING- GENERATICN OF X/Y COORDI IATES FOR CUTTER CENTER 0.

OFFSETTING TO THE CUTTER POSITION FROM THE CAM FOLLOWER CENTEP I5 PERFORMED BY DROPPING A PERPENDICULAR TO A CHORD IN THE SA E TANNER AS BEFORE. THE X/Y COORDINATE REFERENCE Sr'5TE IS SUCH THAT THE CUTTEQ GENERATING THE CAM SURFACE FOR T"!E CA' FOLLOWER IN THE CENTER-OF-YANKEE PGSI TION IS ON THE -X A XIS- THUS THE CUTTEQ AT ITS STARTINS/ENDINIJ POSITICA a ILL BE ON THF +X AXIS- X I 1 l -R 1 l-CORR NOTE THAT (NOWING THE QADIUS E X/Y POITION IS FOUND BY GENE'QAT IiG AN ANGLE FRG Th6 .L'1BER OF STEPS TIMES THi CA? ANGLE CF RCTATIC\ PER STEP.

vow

XX 2 (GS E PI-ST RAI W qwwsMwl-srmm DO 32 J=2 0N X (J) XX-QAT*KYNX-YPR XX I XNX YY I YNX 32 CONTINUE A l ls Fi'I TH:

l xCnC l END OF JDP-aueceocun OUTPUTTING ERROR ESSAGES a o n STU END

EVD

Having described the preferred embodiment of the invention, it is to be recognized that the invention includes within its scope modifications and variations of the preferred embodiment. For example, a rigid grinding wheel with the periphery contour of the invention could be substituted for the backstand grinder, and

many of the advantages of the invention would still be retained. Also, the contoured periphery contact wheel of the invention could be advantageously used alone without the new unique cam. Furthermore, the use of the new unique cam of the invention without the contoured periphery contact wheel is also advantageous because of time savings, greater precision, and avoidance of overgrinding the drier drum. It should also be recognized that the invention is not limited to the cam controlling the grinder movement with respect to the drum by pivoting the grinder about the carriage. The cam could also control the movement through slides, linkages, or other mechanisms, and the grinder can move in a manner other than pivoting. Of course, the method of calculating cam advantage set out in the preferred embodiment would be modified to apply to the particular mechanisms used. With any of these mechanisms, the cam can be mounted in places other than on NSC-RM UUTPUTS A.

SUGGEST HIE-RUN WITH S =ALLEQ DlS l AY HAVE TO RE INCREASED TO commas/=15.

CUTTEQ I O?) NCTE Di 7] OF PRQGRA OUTLINEICIIII'III ERRCR ESSAGE SHOULD APPEA? AS FOLLOWS. s 0

EXTEND SUFFXC IENTLY BEYOND THE NOTE JOB ENDED.

APPEAR AS FOLLJ-MS- c SLCW:

MAY HAVI: TD

ERROR ESSAGE SHCJULD APPEAR AS FOLLOWS. 0

the carriage. It should also be recognized that the invention could be used to resurface any complex contoured drum, although its special features are most advantageously applied to resurfacing Yankee drier drums.

From the foregoing description, it is apparent that other modifications can be made without departing from the spirit of the invention and the exemplary embodiment is not intended to be limitative of the invention since the scope of the invention is defined in the appended claims.

We claim:

1. Apparatus for forming predetermined complex crown contours on the exterior surface of a large creping and drier drum, whereon the contour of the end regions differs from the contour of the middle region of the drum, comprising:

a carriage;

means for traversing said carriage from end to end of said drier drum;

grinder means rotatable on its axis for forming said crown contours, said grinder means being movably mounted on said carriage and spaced from the axis of said drier drum, said grinder means having an abrasive surface on which the center of the area of contact of the abrasive surface and the drum surface varies across the width of the abrasive surface for different traverse positions of said carriage and the center point of the abrasive surface periphery is spaced from the exterior surface of the drum by distance which varies for different traverse positions of said carriage; and cam means for causing movement of said grinder means with respect to said carriage to vary said spacing between said grinder means and said axis of said drier drum, said cam means including a cam contoured in a predetermined relationship to the predetermined crown contours to be formed on the end regions and the middle region of the surface of said drier drum and contoured to compensate for the change in distance between the center point of the abrasive surface periphery and the exterior surface of the drum resulting from the contour of the exterior surface of the drum. 2. Apparatus according to claim I, wherein said grinder means includes a convex surface presented to contact with the drum surface at all positions of the drum surface.

3. Apparatus according to claim 1, wherein said grinder means includes a convex surface contoured to have a slope equal to the slope of said drum surface contour at the center of the area of contact of the grinder and drum surface at all positions of the drum surface while the grinder means axis is maintained parallel to the drum axis.

4. Apparatus for forming predetermined complex crown contours on the surface of a large creping and drier drum, whereon the contour of the end regions differs from the contour of the middle region of the drum, comprising:

a carriage; means for traversing said carriage along a predetermined path parallel to the axis of said drier drum;

grinder means mounted on said carriage for forming said crown contour, including an abrasive surface rotatable about an axis, means to rotate said abrasive surface, and means to press said abrasive surface against said surface of said drier drum, the center of the area of contact of the abrasive surface and the drum surface varying across the width of the abrasive surface for different traverse positions of said carriage and the center point of the abrasive surface periphery being spaced from the surface of the drum by distance which varies for different traverse positions of said carriage; and

means for varying the spacing between said grinder means and said drier drum axis, comprising a cam follower mounted on said grinder means, a cam cooperating with said cam follower and rotatably mounted on said carriage and contoured to vary said spacing in a predetermined relationship to said predetermined crown contours to be formed from end to end on said surface of said drier drum and contoured to compensate for the change in spacing between the center point of the abrasive surface periphery and the surface of the drum resulting from the contour of the exterior surface of the drum, and means for rotating said cam in a predetermined relationship to the traverse position of said carriage.

5. Apparatus according to claim 4, wherein said means to press said abrasive surface against said surface of said drier drum includes a wheel having a convex periphery contour which has a slope equal to the slope of said drum surface contour at the center of the area of contact of the abrasive surface and drum surface at all positions of said drum surface while said abrasive surface rotational axis is maintained parallel to the drum axis.

6. Apparatus according to claim 5, wherein said periphery contour is a convex circular are having a radius which is substantially equal to the radius determined by the equation:

D( 13) t/S where D( 13) the radius of the periphery contour in inches,

1 the distance from the center of the face of the contact wheel to the desired contact point of the contact wheel and the drum surface where the drum surface contour has the greatest slope, in inches, and

S the greatest slope on the surface contour of the drum in inches per inch.

7. Apparatus for forming predetermined complex crown contours on the exterior surface of a large creping and drier drum, whereon the contour of the end regions differ from the contour of the middle region of the drum, comprising:

a carriage;

means for traversing said carriage from end to end of said dryer drum;

grinder means rotatable on its axis for forming said crown contours, said grinder means being movably mounted on said carriage and spaced from the axis of said drier drum, said grinder means including a convex surface contoured to have a slope equal to the slope of said drum surface contour at the center of the area of contact of the grinder means and drum surface at all positions of the drum surface while the grinder means axis is maintained parallel to the drum axis; and

cam means for causing movement of said grinder means with respect to said carriage to vary said spacing between said grinder means and said axis of said drier drum, said cam means including a cam contoured in a predetermined relationship to the predetermined crown contours to be formed on the end regions and the middle region of the surface of said drier drum.

8. Apparatus for forming predetermined complex crown contours on the surface of a large creping and drier drum, whereon the contour of the end regions differs from the contour of the middle of the drum, comprising:

a carriage;

means for traversing said carriage along a predetermined path parallel to the axis of said drier drum;

grinder means mounted on said carriage for forming 

1. Apparatus for forming predetermined complex crown contours on the exterior surface of a large creping and drier drum, whereon the contour of the end regions differs from the contour of the middle region of the drum, comprising: a carriage; means for traversing said carriage from end to end of said drier drum; grinder means rotatable on its axis for forming said crown contours, said grinder means being movably mounted on said carriage and spaced from the axis of said drier drum, said grinder means having an abrasive surface on which the center of the area of contact of the abrasive surface and the drum surface varies across the width of the abrasive surface for different traverse positions of said carriage and the center point of the abrasive surface periphery is spaced from the exterior surface of the drum by distance which varies for different traverse positions of said carriage; and cam means for causing movement of said grinder means with respect to said carriage to vary said spacing between said grinder means and said axis of said drier drum, said cam means including a cam contoured in a predetermined relationship to the predetermined crown contours to be formed on the end regions and the middle region of the surface of said drier drum and contoured to compensate for the change in distance between the center point of the abrasive surface periphery and the exterior surface of the drum resulting from the contour of the exterior surface of the drum.
 2. Apparatus according to claim 1, wherein said grinder means includes a convex surface presented to contact with the drum surface at all positions of the drum surface.
 3. Apparatus according to claim 1, wherein said grinder means includes a convex surface Contoured to have a slope equal to the slope of said drum surface contour at the center of the area of contact of the grinder and drum surface at all positions of the drum surface while the grinder means axis is maintained parallel to the drum axis.
 4. Apparatus for forming predetermined complex crown contours on the surface of a large creping and drier drum, whereon the contour of the end regions differs from the contour of the middle region of the drum, comprising: a carriage; means for traversing said carriage along a predetermined path parallel to the axis of said drier drum; grinder means mounted on said carriage for forming said crown contour, including an abrasive surface rotatable about an axis, means to rotate said abrasive surface, and means to press said abrasive surface against said surface of said drier drum, the center of the area of contact of the abrasive surface and the drum surface varying across the width of the abrasive surface for different traverse positions of said carriage and the center point of the abrasive surface periphery being spaced from the surface of the drum by distance which varies for different traverse positions of said carriage; and means for varying the spacing between said grinder means and said drier drum axis, comprising a cam follower mounted on said grinder means, a cam cooperating with said cam follower and rotatably mounted on said carriage and contoured to vary said spacing in a predetermined relationship to said predetermined crown contours to be formed from end to end on said surface of said drier drum and contoured to compensate for the change in spacing between the center point of the abrasive surface periphery and the surface of the drum resulting from the contour of the exterior surface of the drum, and means for rotating said cam in a predetermined relationship to the traverse position of said carriage.
 5. Apparatus according to claim 4, wherein said means to press said abrasive surface against said surface of said drier drum includes a wheel having a convex periphery contour which has a slope equal to the slope of said drum surface contour at the center of the area of contact of the abrasive surface and drum surface at all positions of said drum surface while said abrasive surface rotational axis is maintained parallel to the drum axis.
 6. Apparatus according to claim 5, wherein said periphery contour is a convex circular arc having a radius which is substantially equal to the radius determined by the equation: D(13) t/S where D(13) the radius of the periphery contour in inches, t the distance from the center of the face of the contact wheel to the desired contact point of the contact wheel and the drum surface where the drum surface contour has the greatest slope, in inches, and S the greatest slope on the surface contour of the drum in inches per inch.
 7. Apparatus for forming predetermined complex crown contours on the exterior surface of a large creping and drier drum, whereon the contour of the end regions differ from the contour of the middle region of the drum, comprising: a carriage; means for traversing said carriage from end to end of said dryer drum; grinder means rotatable on its axis for forming said crown contours, said grinder means being movably mounted on said carriage and spaced from the axis of said drier drum, said grinder means including a convex surface contoured to have a slope equal to the slope of said drum surface contour at the center of the area of contact of the grinder means and drum surface at all positions of the drum surface while the grinder means axis is maintained parallel to the drum axis; and cam means for causing movement of said grinder means with respect to said carriage to vary said spacing between said grinder means and said axis of said drier drum, said cam means including a cam contoured in a predetermined relationship to the predetermined crown contoUrs to be formed on the end regions and the middle region of the surface of said drier drum.
 8. Apparatus for forming predetermined complex crown contours on the surface of a large creping and drier drum, whereon the contour of the end regions differs from the contour of the middle of the drum, comprising: a carriage; means for traversing said carriage along a predetermined path parallel to the axis of said drier drum; grinder means mounted on said carriage for forming said crown contour, including a rotatable abrasive surface, means to rotate said abrasive surface about an axis, and means to press said abrasive surface against said surface of said drier drum, said means to press said abrasive surface against said surface of said drier drum includes a wheel having a convex periphery contour which has a slope equal to the slope of said drum surface contour at the center of the area of contact of the abrasive surface and drum surface at all positions of said drum surface while said abrasive surface rotational axis is maintained parallel to the drum axis; and means for varying the spacing between said grinder means and said drier drum axis, comprising a cam follower mounted on said grinder means, a cam cooperating with said cam follower and rotatably mounted on said carriage and contoured to vary said spacing in a predetermined relationship to said predetermined crown contours to be formed from end to end on said surface of said drier drum, and means for rotating said cam in a predetermined relationship to the traverse position of said carriage.
 9. Apparatus according to claim 8, wherein said contoured periphery of said wheel is resilient. 